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JEE MATHEMATICS MCQ: PAIR OF STRAIGHT LINES

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If the equation λx2+4xy+5y2=0\lambda x^2+4 x y+5 y^2=0 represents two lines inclined at an angle π\pi, then λ=\lambda=
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Correct option: B
4/54 / 5
Option B (4/54 / 5) is correct because for the lines to be inclined at an angle π\pi, they must be coincident, implying h2−ab=0h^2 - ab = 0, which leads to λ=4/5\lambda = 4/5.

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If ax2+2hxy+by2+2gx+2fy+c=0a x^2+2 h x y+b y^2+2 g x+2 f y+c=0 represents parallel straight lines, then Image of the point (−1,3)(-1,3) with respect to the line y=2xy=2 x is If the pair of lines represented by ax2+2hxy+by2+2gx+2fy+c=0a x^2+2 h x y+b y^2+2 g x+2 f y+c=0 intersect on yy-axis, then If the sum of the slopes of the lines given by 4x2+2λxy−7y2=04 x^2+2 \lambda x y-7 y^2=0 is equal to the product of the slopes, then λ\lambda is equal to The equation 3x2+2hxy+3y2=03 x^2+2 h x y+3 y^2=0 represents a pair of straight lines passing through the origin. The two lines are The value of hh for which 3x2−3hxy+4y2=03 x^2-3 h x y+4 y^2=0 represents a pair of coincident lines are
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